I have to do searches for my downloads at times, Seedcorn.
The computer just puts them where you last decided something should go. Fortunately, Firefox at least asks me what I want to name them. Then, I'd better go looking for them right away while I still remember that name if I didn't check where they were going.
You might think that computer would be smart enuf to put downloads in "Downloads!" But no! I have inadvertently downloaded pictures even to "Music!" Sheesh!
Click on downloads in your browser to open the download history. Right click and choose open containing folder, then find it. Or re-DL the pic and this time choose where to DL and not let the PC place it just anywhere. I always choose my desktop and then move it, if it's not there when I minimize the browser, I check the DL history.